Our increasingly integrated world relies on networks both physical and virtual to transfer goods and information. The Internet is a network of networks that connects people around the world in a real-time manner, but it can be disrupted by massive data flows, diverse traffic patterns, inadequate infrastructure, and even natural disasters and political conflict. Similar challenges exist for transportation and energy distribution networks. There is an urgent need for intelligent and adaptable routing of network flows, and a rich literature has evolved that treats "oblivious network design." This book offers novel computational schemes for efficiently solving routing problems in unpredictable circumstances and proposes some real world applications for them. The versatile routing schemes mathematically guarantee long-term efficiency and are most appropriate for networks with non-deterministic (or oblivious) current and past states. After an introduction to network design and the importance of routing problems, the book presents mathematical tools needed to construct versatile routing schemes, emphasizing the role of linked hierarchical data structures, both top-down and bottom-up. It then describes two important applications of versatile routing schemes: a secure model for congestion-free content-centric networks (which will play a key role in the future of the Internet) and a novel approach for the distribution of green power resources on a smart electricity grid.